Theoretical Statistics and Mathematics Unit, ISI Delhi

Torus equivariant spectral triple for quantum quaternion sphere

by Bipul Saurabh

We give an explicit description of the $q$-deformation of symplectic group $SP_{q}(2n)$ at the $C^*$-algebra level and find all irreducible representations of this $C^{*}$-algebra. Further we study its Stiefel manifold $SP_{q}(2n)/SP_q(2n-2)$ by getting its defining relations and describe its irreducible representations. We compute its $K$-theory by obtaining a chain of short exact sequence for the $C^{*}$-algebras underlying such manifolds. The torus group $\mathbb{T}^{n}$ has a canonical action on $C(SP_{q}(2n)/SP_{q}(2n-2))$. We find a non-trivial, finitely summable equivariant spectral triple associated with this action.

isid/ms/2014/03 [fulltext]

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